Problem #1 - pins 0 and 1 are used for Serial. You can not use them for your software SPI at the same time. rewire your board to use pins 2 and 3 or any other free pins.
#include "LCD16x2.h"
Link to this library? It is not in the IDE library manager list. Typically a display needs a .begin() function to get it up and running. I do not see that in your code. Is the display connected by i2c (aka Wire)?
analogWrite(RELAY_PIN, 0);
If this truly is a relay, it will never function at PWM frequencies. Relays are more of a digital switch. If you do need to turn something on/off that rapidly, you need to use a logic level MOSFET
interrupt_trigger_flag
check_buttons_flag
button_changed_flag
Are these variables declared in "coffee_roaster.h"? If so, you need to post that code as well.
I think your code could be improved if you google "Finite State Machine" and apply some of those learnings. The code has some transition states and some regular state. In the very basic framework, you have 3 functions. beginState(), updateState() and endState(). Each of these functions contains a case/switch statement to deal with the state variabled passed in
beginState - do whatever is necessary at the start of a new state. Update the global 'currentState' variable
updateState - check elapsed time or sensors or button states and possibly transition to a new state
endState - do whatever needs to happen when a state is about to exit
Then, you loop looks like this
void loop() {
currentTime = millis();
if ( currentTime - lastSampleTime >= sampleInterval ) {
lastSampleTime = currentTime;
readSensors();
}
readButtons();
checkSerialInput();
updateState(currentState);
}
I would also suggest you remove about 90% of those sprintf() statements everywhere in the code, except for in the lcd routines that actually display the values. Those other routines can just deal with the floating point number directly, etc. The function that displays them should be the function that formats them.